Method for forming a high resolution image by lensless imaging

ABSTRACT

A device and method for forming an image of a sample includes illuminating the sample with a light source; acquiring a plurality of images of the sample using an image sensor, the sample being placed between the light source and the image sensor, no magnifying optics being placed between the sample and the image sensor, the image sensor lying in a detection plane, the image sensor being moved with respect to the sample between two respective acquisitions, such that each acquired image is respectively associated with a position of the image sensor in the detection plane, each position being different from the next; and forming an image, called the high-resolution image, from the images thus acquired.

TECHNICAL FIELD

The invention belongs to the technical field of lensless imaging, forthe observation of samples, in particular biological samples. Lenslessimaging consists in observing a sample placed between a light source andan image sensor, the sample being placed in proximity to the imagesensor, without any magnifying optics between the sensor and the sample.

PRIOR ART

The observation of samples, and in particular biological samples, bylensless imaging has seen substantial development over the last 10years. This technique allows a sample to be observed by placing itbetween a light source and an image sensor, without placing anymagnifying optical lenses between the sample and the sensor. Thus, theimage sensor collects an image of the light wave transmitted by thesample.

This image is formed from interference patterns generated byinterference between the light wave emitted by the source andtransmitted without diffraction by the sample, and diffracted wavesresulting from the diffraction, by the sample, of the light wave emittedby the source. These interference patterns are sometimes calleddiffraction patterns, or holograms.

Document WO2008090330 describes a device allowing biological samples, infact cells, to be observed by lensless imaging. The device makes itpossible to associate, with each cell, one interference pattern, themorphology of which allows the type of cell to be identified. Lenslessimaging would therefore appear to be a simple and inexpensivealternative to a conventional microscope. In addition, its field ofobservation is clearly larger than it is possible for that of amicroscope to be. It will thus be understood that the perspectiveapplications of this technology are many and important.

The image formed on the image sensor, which contains interferencepatterns, may be processed by a numerical propagation algorithm, so asto estimate the optical properties of the sample. Such algorithms arewell known in the field of holographic reconstruction. To do this, thedistance between the sample and the image sensor being known, apropagation algorithm, taking into account this distance, and thewavelength, is applied. It is thus possible to reconstruct an image ofan optical property of the sample. One numerical reconstructionalgorithm is for example described in US2012/0218379.

U.S. Pat. No. 8,866,063, by the same author as the aforementioned patentapplication, describes a method allowing the spatial resolution ofimages obtained by lensless imaging to be improved. To do this, thesample and the image sensor remaining stationary, a plurality of imagesare acquired such that between each image, the light source is offsetslightly. An image-processing algorithm then allows an image, ofimproved resolution, to be formed by combining the images thus acquired.A method for improving the spatial resolution of an image is alsodescribed in US2016/334614.

The inventors have identified an alternative solution, allowing thespatial resolution of images obtained by lensless imaging to beimproved, using a simple and inexpensive device.

SUMMARY OF THE INVENTION

One subject of the invention is a method for forming an image of asample comprising the following steps:

-   -   a) illuminating the sample with a light source;    -   b) acquiring a plurality of images of the sample using an image        sensor, the sample being placed between the light source and the        image sensor, such that:        -   the sample is immobile with respect to the light source;        -   no magnifying optics are placed between the sample and the            image sensor;        -   the image sensor lies in a detection plane, the image sensor            being moved, in the detection plane, between two successive            acquisitions;        -   each acquired image is respectively associated with a            position of the image sensor in the detection plane, each            position being different from the next;    -   c) calculating a movement of each acquired image with respect to        a reference image in which the image sensor occupies a reference        position;    -   d) forming an image, called the high-resolution image, from the        acquired images and the movement calculated for each thereof.

According to one embodiment, each acquired image contains pixels, andthe high-resolution image contains more pixels than each acquired image.

Thus, contrary to the prior art, the sample remains stationary withrespect to the light source. The light wave reaching the detection planeis therefore identical during each image acquisition. The image sensorforms a different image of this light wave in each acquisition.

The method may comprise one of the following features, whether singly orin any technically possible combination:

-   -   the image sensor is securely fastened to a piezoelectric        transducer, the movement of the position of said image sensor        being generated by activation of said piezoelectric transducer;    -   the movement of the image sensor between two successive        positions is random;    -   each acquired image containing a plurality of pixels, the        maximum value of the movement between two successive images is 5        times or 10 times the distance between two adjacent pixels. This        allows the useful field of observation to be maximized, the        latter corresponding to the intersection of the fields of        observation of each acquired image;    -   the sample contains diffracting elements, each image acquired by        the image sensor containing elementary diffraction patterns,        each elementary diffraction pattern being associated with one        diffracting element of the sample.

According to one embodiment, the method comprises a step e) of applyinga numerical propagation operator to the resulting image, and determininga complex amplitude of a light wave to which the image sensor isexposed.

According to one embodiment, step d) comprises the following substeps:

-   -   i) obtaining a subpixelated image from each acquired image, the        subpixelated image containing a number of pixels higher than the        number of pixels of the acquired image, so as to obtain a stack        of subpixelated images;    -   ii) using the movements determined in step c), aligning each        subpixelated image so as to obtain a stack of subpixelated and        aligned images;    -   iii) combining the subpixelated and aligned images in order to        obtain the high-resolution image.

In substep ii), the alignment may be carried out with respect to a baseimage, the base image being an image taken from the stack ofsubpixelated images formed in substep i).

According to another embodiment, step d) comprises the followingsubsteps:

-   -   i) using the movements determined in step c), aligning each        acquired image so as to obtain a stack of aligned images;    -   ii) obtaining an aligned and subpixelated image from each        aligned image obtained in substep i), the aligned and        subpixelated image containing a number of pixels higher than the        number of pixels of the aligned image, so as to obtain a stack        of aligned and subpixelated images;    -   iii) combining the aligned and subpixelated images in order to        obtain the high-resolution image.

In substep i), the alignment may be carried out with respect to a baseimage, the base image being an image acquired in step b).

According to one embodiment, step d) comprises the following substeps:

-   -   i) aligning each acquired image using the movement that is        associated therewith, so as to obtain an aligned image from each        acquired image;    -   ii) combining each aligned image to form the high-resolution        image.

Another subject of the invention is a device for producing an image of asample comprising:

-   -   a light source, able to illuminate the sample;    -   an image sensor, the sample being placed between the light        source and the image sensor;    -   the image sensor being able to form an image, in a detection        plane, of a light wave transmitted by the sample under the        effect of the illumination by said light source, no magnifying        optics being placed between the image sensor and the sample;        characterized in that the device also comprises:    -   a piezoelectric transducer able to induce a movement of the        image sensor in the detection plane.

The device may also comprise a processor that is able to process aplurality of acquired images of the sample, each image beingrespectively associated with a position of the image sensor in thedetection plane, each position being different from the next, theprocessor being able to implement steps c) and d) of a method such asdescribed in this patent application.

The device may be such that the image sensor is translationallyimmovable along the propagation axis of the light emitted by the lightsource.

FIGURES

FIG. 1 shows an example of a device according to the invention.

FIG. 2 shows the main steps of a method according to the invention.

FIGS. 3A, 3B and 3C show three successive positions of the image sensorwith respect to a sample.

FIG. 4 illustrates the successive movements of the image sensor during afirst experimental trial.

FIGS. 5A, 5B, and 5C respectively show, in relation to the firstexperimental trial, an acquired image, the subpixelated acquired image,and a so-called high-resolution image obtained by combining 16subpixelated and aligned images.

FIGS. 6A and 6B show an intensity profile of the pixels on a line drawnin FIGS. 5A and 5C, respectively.

FIG. 7A is an image obtained by applying a holographic propagationoperator to the image of FIG. 5A. FIG. 7B is a detail of FIG. 7A.

FIG. 7C is an image obtained by applying a holographic propagationoperator to the image of FIG. 5C. FIG. 7D is a detail of FIG. 7C.

FIG. 8A is an image acquired by an image sensor during a secondexperimental trial. FIG. 8B is a detail of FIG. 8A. FIG. 8C is ahigh-resolution image formed during the second experimental trial,including the acquisition of 16 successive images. FIG. 8D is a detailof FIG. 8C. FIG. 8E shows the movement of the image sensor between eachof the 16 images acquired during the second experimental trial.

DESCRIPTION OF PARTICULAR EMBODIMENTS

FIG. 1 shows an example of a device according to the invention. A lightsource 11 is able to emit a light wave 12, called the incident lightwave, that propagates in the direction of a sample 10, along apropagation axis Z. The light wave is emitted in a spectral band Δλ.

The sample 10 is a sample that it is desired to characterize. It maynotably be a question of a medium 10 a containing particles 10 b. Theparticles 10 b may be blood cells, for example red blood cells or whiteblood cells. It may also be a question of other cells, ofmicroorganisms, for example bacteria or yeast, of microalgae, ofmicrospheres, or of droplets that are insoluble in the liquid medium,lipid nanoparticles for example. Preferably, the particles 10 b have adiameter, or are inscribed in a diameter, smaller than 1 mm, andpreferably smaller than 100 μm. They are microparticles (diametersmaller than 1 mm) or nanoparticles (diameter smaller than 1 μm). Themedium 10 a, in which the particles are submerged, may be a liquidmedium, for example a liquid phase of a bodily liquid, a culture mediumor a liquid sampled from the environment or from an industrial process.It may also be a solid medium or a medium having the consistency of agel, for example an agar substrate, propitious to the growth ofbacterial colonies. The sample 10 may also be a tissue slide, ofpathology-slide type.

The sample 10 is contained in a fluidic chamber 15. The fluidic chamber15 is for example a microcuvette, commonly used in point-of-care typedevices, in which the sample 10 penetrates, for example by capillaryaction. The thickness e of the sample 10, along the propagation axis,typically varies between 20 μm and 1 cm, and is preferably comprisedbetween 50 μm and 500 μm, 100 μm for example.

The sample lies in a plane P₁₀, called the plane of the sample,perpendicular to the propagation axis. It is held on a holder 10 s.

The distance D between the light source 11 and the sample 10 ispreferably larger than 1 cm. It is preferably comprised between 2 and 30cm. Preferably, the light source, seen from the sample, may beconsidered to be point-like. This means that its diameter (or itsdiagonal) is preferably smaller than one tenth, better still onehundredth, of the distance between the sample and the light source.Thus, preferably, the light reaches the sample in the form of planewaves, or waves that may be considered to be such.

The light source 11 may be a light-emitting diode or a laser diode. Itmay be associated with a diaphragm 18, or spatial filter, the use ofsuch a spatial filter not being necessary when the light source is alaser source. The aperture of the diaphragm is typically comprisedbetween 5 μm and 1 mm, and preferably between 50 μm and 500 μm. In thisexample, the diaphragm is supplied by Thorlabs under the reference P150Sand its diameter is 150 μm. The diaphragm may be replaced by an opticalfiber, a first end of which is placed facing the light source 11 and asecond end of which is placed facing the sample 10.

The device preferably comprises a diffuser 17, placed between the lightsource 11 and the diaphragm 18 in particular when the light source is alight-emitting diode. The use of such a diffuser allows constraints onthe centrality of the light source 11 with respect to the aperture ofthe diaphragm 18 to be avoided. The function of such a diffuser is todistribute the light beam produced by the elementary light source 11over a cone of angle α, α being equal to 60° in the present case.Preferably, the diffusion angle varies between 10° and 90°.

Preferably, the spectral emission band Δλ, of the incident light wave 12has a width smaller than 100 nm. By spectral bandwidth, what is meant isa full width at half maximum of said spectral band.

The sample 10 is placed between the light source 11 and an image sensor16. The latter preferably lies parallel, or substantially parallel, tothe plane in which the sample lies. The term substantially parallelmeans that the two elements may not be rigorously parallel, an angulartolerance of a few degrees, lower than 20° or 10°, being acceptable.

The image sensor 16 is able to form an image in a detection plane P₀. Inthe example shown, it is an image sensor comprising a matrix array ofCCD pixels or a CMOS sensor. Each pixel is designated 16 r, rrepresenting a coordinate of the pixel in the detection plane. CMOSsensors are preferred, because the pixels are of smaller size, thisallowing images to be acquired the spatial resolution of which is morefavorable. The detection plane P₀ preferably lies perpendicular to thepropagation axis Z of the incident light wave 12. The image sensor 16 isplaced in contact with a piezoelectric module 19′ allowing apiezoelectric transducer 19 to be activated, the latter being able tomove, in a plane parallel to the detection plane P₀, when it issubjected to an electrical excitation. The movement of the piezoelectrictransducer 19 causes a movement of the image sensor 16 parallel to thedetection plane P₀.

The distance d between the sample 10 and the matrix array of pixels ofthe image sensor 16 is preferably comprised between 50 μm and 2 cm, andmore preferably comprised between 100 μm and 2 mm. Preferably, thisdistance is kept constant, translation of the image sensor 16 along thepropagation axis Z, i.e. perpendicular to the detection plane P₀, beingblocked. The translational blockage may be obtained by straps that blockor limit a translation of the image sensor along the axis Z.

The absence of any magnifying optics between the image sensor 16 and thesample 10 will be noted. This does not prevent focusing micro-lensesoptionally being present level with each pixel of the image sensor 16,these lenses not having the function of magnifying the image acquired bythe image sensor.

Under the effect of the incident light wave 12, the sample 10 maygenerate a diffracted wave, liable to produce, on the detection planeP₀, interference, in particular with a portion of the incident lightwave 12 transmitted by the sample. Moreover, the sample may absorb someof the incident light wave 12. Thus, the light wave 22, transmitted bythe sample, and to which the image sensor 16 is exposed, may comprise:

-   -   a component resulting from diffraction of the incident light        wave 12 by the sample; and    -   a component resulting from transmission of the incident light        wave 12 by the sample.

Under the effect of the diffraction, each particle 10 b present in thesample may give rise to the formation of a diffraction pattern, orhologram, in the image acquired by the image sensor 16. Such a hologramgenerally takes the form of a light central spot encircled byalternatively light and dark diffraction rings. The higher the spatialresolution of the hologram, the better the possibilities with respect tocharacterization of the particle, notably when holographicreconstruction algorithms such as described below are used.

A processor 20, for example a microprocessor, is able to process eachimage acquired by the image sensor 16. In particular, the processor is amicroprocessor connected to a programmable memory 22 in which a sequenceof instructions for carrying out the image-processing and calculatingoperations described in this description is stored. The processor may becoupled to a screen 24 allowing the images acquired by the image sensor16 or calculated by the processor 20 to be displayed.

The invention is based on the observation that a single image of asample 10 may have a spatial resolution that is insufficient for aprecise characterization of the particles 10 b. Just as in the methoddescribed with reference to the prior art, a plurality of images of thesample are successively acquired. However, contrary to the prior art,the relative position of the sample 10 with respect to the light source11 is kept constant, whereas the relative position of the image sensor16 with respect to the sample 10 varies between the acquisition of twosuccessive images. More precisely, between each image acquisition, thepiezoelectric transducer 19 is activated, so as to move the image sensorparallel to the detection plane P₀. The movement may be random, thisallowing a simple and inexpensive piezoelectric transducer to be used,since the vector characterizing the movement in the detection plane P₀may be determined as described below. Contrary to the prior art, therelative position of the analyzed sample 10 and of the light source 11does not vary between two successive acquisitions. Thus, the same imageis projected onto the detection plane P₀, which is not the case when thelight source is moved with respect to the sample 10, or vice versa.Specifically, the inventors believe that it is preferable to carry out aplurality of acquisitions of the image projected onto the detectionplane, the position of the image sensor being modified between eachacquisition, so as to obtain a plurality of acquisitions of a givenimage projected onto the detection plane, these acquisitions beingobtained with the image sensor in different positions in the detectionplane. The combination of these acquisitions allows an image I_(HR),called the high-resolution image, having an improved spatial resolutionto be obtained.

The main steps of a formation of the high-resolution image are describedbelow, with reference to FIG. 2:

Step 100:

Initialization; illumination of the sample 10 with the matrix-arraysensor placed in an initial position (x₀, y₀) in the detection plane P₀.The initial position of the image sensor corresponds to a position of areference point of this sensor, for example the position of one pixel.It may for example be a position of the center of the image sensor, orof one of its edges.

Step 110:

Acquisition of an image. In the first iteration, an initial imageI_(i=0) associated with the initial position (x_(i=0), y_(i=0)) of theimage sensor is acquired in the detection plane.

Step 120:

Provided that a criterion for exiting the iterations has not been met,pulsed activation of the piezoelectric transducer 19, so as to modifythe position of the image sensor in the detection plane, the latterpassing from a position (x_(i), y_(i)) to a position (x_(i+1), y_(i+1))and repetition of step 110 with update of the index of iteration i. Thelatter is an integer. Once the criterion for exiting the iterations ismet, step 130 is passed to. The criterion for exiting the iterations isfor example a preset number N_(i) of acquired images. Step 120 allows astack of acquired images I_(i) to be obtained, with 2≤i≤N_(i). Thenumber of acquired images may vary between 2 and 20. The expression“pulsed activation” means a brief activation, the duration of which isgenerally shorter than 1 second, and typically of about a few tens ofmilliseconds, followed by a period of rest in which an image may beacquired.

FIGS. 3A, 3B and 3C show three different positions of the image sensor16 with respect to a sample 10 containing three particles 10 b. Becausethe light source is immobile with respect to the sample, the imageprojected into the detection plane is rigorously identical: theprojection of each particle into the detection plane remains stationary.In these figures, the image sensor has been represented by a griddelineating the pixels 16 r of the sensor. The movement of the sensormakes it possible to make the projection of each particle 10 b, alongthe propagation axis Z, vary with respect to the image sensor 16. Thus,the relative position of each particle with respect to one pixel of thedetector is modified on each movement of the image sensor.

The movement of the sensor, between two successive images, is preferablysmaller than 5 pixels, or than 10 pixels. The useful field ofobservation, corresponding to the stack of acquired images, is theintersection of the field of observation of each image. Thus, thelimitation of the movement of the sensor to a few pixels allows thefield of observation to be maximized.

Step 130:

Estimation of the movement Δ_(i) of each image I_(i) with respect to areference image I_(ref-i). The reference image I_(ref-i) may, forexample, be the initial image I₀ or the image I_(i−1) acquired beforeeach image I_(i). With the reference image is associated a referenceposition (x_(ref-i), y_(ref-i)) of the image sensor 16. The referenceimage I_(ref-i) may be the same for each acquired image, in which caseit is denoted I_(ref). Each movement is calculated with respect to thesame reference position, such that (x_(ref-i), y_(ref-i))=(x_(ref),y_(ref)). It has been observed that the results are optimal when, foreach image I_(i), the reference image I_(ref-i) is the initial image I₀.In other words, when I_(ref)=I₀.

The movement Δ_(i) of an image I_(i) is a vector the coordinates ofwhich represent a movement between the reference image I_(ref-i) and theacquired image I_(i), and more particularly a translation in thedetection plane.

A plurality of methods are known for estimating the movement of twoimages with respect to each other. In the case where the movement isrestricted to a translation in a plane, the inventors have implemented amethod based on a ratio between the Fourier transforms of the acquiredimage I_(i) in question and of the reference image I_(ref-i), so as toestimate a movement by an integer number of pixels, this being followedby an estimation of a so-called subpixel movement smaller than the sizeof one pixel. Step 130 then comprises the following substeps:

Substep 131: calculation of the Fourier transforms of the acquired imageI_(i) and reference image I_(ref-i).

Substep 132: calculation, term by term, of a product of the two Fouriertransforms calculated in substep 131, so as to obtain a resulting imageI_(i/ref-i) such that:

$I_{{i/{ref}} - i} = \frac{{{FT}\left( I_{i} \right)}{{FT}^{*}\left( I_{{ref} - i} \right)}}{{{{FT}\left( I_{i} \right)}{{FT}^{*}\left( I_{{ref} - i} \right)}}}$

-   -   where FT represents the Fourier transform operator, the latter        for example being calculated using a fast Fourier transform        (FFT) algorithm, and FT* represents the operator returning the        conjugate Fourier transform.

Substep 133: calculation of an inverse Fourier transform of theresulting image I_(i/ref_i) obtained in the preceding substep. An imagethe maximum intensity of which corresponds to a point (Δx_(i), Δy_(i))is obtained, Δx_(i) and Δy_(i) being the coordinates of the vectorrepresenting the sought movement Δ_(i) by an integer number of pixels inthe two directions of the detection plane P₀. Δx_(i) and Δy_(i) areintegers. Thus, seeking the point of maximum intensity in the image,obtained by inverse Fourier transform of the resulting imageI_(i/ref-i), allows the integer coordinates Δx_(i) and Δy_(i) of thesought movement Δ_(i) to be obtained.

Substep 134: estimation of the subpixel movement. The movement Δ_(i) maycomprise a non-integer component, expressing the movement, called thesubpixel movement, of the acquired image I_(i) in a non-integer numberof pixels lower than 1. The quantities dx_(i) and dy_(i) respectivelydesignate a subpixel movement in one of the two directions of thedetection plane P₀.

The acquired image I_(i) may be corrected using the integer coordinatesΔx_(i) and Δy_(i) determined in substep 133, so as to form anintermediate image I_(i) ^(Δx) ^(i) ^(Δ) ^(i) corrected for the movementby Δx_(i) and Δy_(i):I_(i) ^(Δx) ^(i) ^(Δi) ^(i) (x, y)=I_(i)(x−Δx_(i);y−Δy_(i)).

If I_(i) ^(Δ) ^(t) is the image corrected for the movement Δ_(i), whereΔ_(i)=(Δx_(i)+dx_(i); Δy_(i)+dy_(i)), assuming subpixel movements dx_(i)and dy_(i) allows a linear relationship between the intermediate imageI_(i) ^(Δx) ^(i) ^(Δy) ^(i) and the corrected image I_(i) ^(Δ) ^(i) tobe obtained, such that:

I_(i)^(Δ_(i))(x, y) = I_(i)^(Δ x_(i)Δ y_(i))(x + dx_(i), y + dy_(i))                  ${I_{i}^{\Delta_{i}}\left( {x,y} \right)} = {{I_{i}^{\Delta\; x_{i}\Delta\; y_{i}}\left( {x,y} \right)} + {{dx}*\frac{{dI}_{i}^{\Delta\; x_{i}\Delta\; y_{i}}}{dx}\left( {x,y} \right)} + {{dy}*\frac{{dI}_{i}^{\Delta\; x_{i}\Delta\; y_{i}}}{dy}\left( {x,y} \right)}}$

The error E_(i)(dx, dy) between the images I_(i) ^(Δx) ^(i) ^(Δy) ^(i)and I_(i) ^(Δ) ^(i) may be written:

${E_{i}\left( {{dx},{dy}} \right)} = {\int{\left( {{I_{i}^{\Delta_{i}}\left( {x,y} \right)} - {I_{i}^{\Delta\; x_{i}\Delta\; y_{i}}\left( {x,y} \right)} - {{dx}*\frac{{dI}_{i}^{\Delta\; x_{i}\Delta\; y_{i}}}{dx}\left( {x,y} \right)} - {{dy}*\frac{{dI}_{i}^{\Delta\; x_{i}\Delta\; y_{i}}}{dx}\left( {x,y} \right)}} \right)^{2}{dxdy}}}$The values dx_(i) and dy_(i) that minimize E_(i)(dx, dy) may beestimated, with

${\frac{dE}{dx}\left( {{dx}_{i},{dy}_{i}} \right)} = 0$ and${\frac{dE}{dy}\left( {{dx}_{i},{dy}_{i}} \right)} = 0$

The estimation of dx_(i) and dy_(i) allows the movementΔ_(i)=(Δx_(i)+dx_(i); Δy_(i)+dy_(i)) to be obtained.

Step 134 is optional. When it is not implemented, the movement Δ_(i) isobtained using the integer coordinates Δx_(i) and Δy_(i) obtainedfollowing substep 133.

Substeps 131 to 134 are repeated for each acquired image I_(i), thereference image I_(ref_i) possibly for example being the initial imageI₀, this being the preferred configuration, or an image I_(i−1) acquiredbeforehand.

FIG. 4 shows the successive movements Δ_(i) of a stack of 16 images, theposition (0,0) corresponding to the coordinate of the initial image I₀.The abscissa and ordinate axes respectively represent the coordinates ofeach movement Δ_(i) along the X- and Y-axes defining a base of thedetection plane P₀.

Step 140:

subpixelation. Each acquired image I_(i) is subpixelated, for example bya factor comprised between 2 and 10. To do this, from each acquiredimage I_(i), an image, called the subpixelated image I_(i,HR),containing more pixels than the acquired image I_(i), is determined. Thesubpixelated image I_(i,HR) may be obtained by dividing each pixel ofthe acquired image I_(i) into N² subpixels, N being an integer higherthan 1. N may for example be equal to 4, this allowing a subpixelatedimage I_(i,HR) containing 16 times more pixels than the acquired imageI_(i) to be obtained. The value of the pixels of the subpixelated imageis calculated by interpolation, for example bilinear or bicubicinterpolation, bicubic interpolation being preferred. A stack ofsubpixelated images I_(i,HR) is thus obtained.

FIG. 5A shows an acquired image I_(i). FIG. 5B shows an example of asubpixelated image I_(i,HR) corresponding to the acquired image shown inFIG. 5A. These images are described more precisely in the rest of thedescription.

Step 150:

alignment. Each subpixelated image is aligned with a subpixelated image,called the base image I_(b,HR), of the stack of subpixelated images. Thebase image is for example the acquired and subpixelated initial image,in which case I_(b,HR)=I_(i=0,HR). Each subpixelated image I_(i,HR) isthen aligned with the base image, by taking into account the movementΔ_(i) associated with the acquired image I_(i), i.e. the movementdetermined in step 130. Thus a stack of subpixelated and aligned images,which images are denoted I_(i,HR) ^(Δ) ^(i) , is obtained.

The base image I_(b,HR) used for the alignment is the same for eachimage I_(i,HR) of the stack of subpixelated images. It may be theinitial image (i=0) or the final image (i=N_(i)) or an image acquiredwhen the image sensor is positioned in a particular position.

Steps 140 and 150 may be inverted, the alignment being carried out withrespect to a base image I_(b) before the subpixelation, so as to obtaina stack of aligned images I_(i) ^(Δ) ^(i) . Each aligned image is thensubpixelated to form a stack of subpixelated and aligned images, whichimages are denoted I_(i,HR) ^(Δ) ^(i) . However, the inventors believethat it is preferable to carry out the alignment after thesubpixelation.

Step 160:

combination of the subpixelated and aligned images I_(i,HR) ^(Δ) ^(i) ,so as to obtain a high-resolution image I_(HR). The high-resolutionimage is obtained via an arithmetic combination of the subpixelated andaligned images I_(i,HR) ^(Δ) ^(i) , for example taking the form of amean, according to the expression:I _(HR)=mean(I _(i,HR) ^(Δ) ^(i) )

If each acquired image contains Nx×Ny pixels, the high-resolution imagecontains N²×Nx×Ny pixels.

The high-resolution image I_(HR) has a spatial resolution higher thaneach of the N_(i) acquired images. This image is used to characterizethe particles 10 b present in the sample. FIG. 5C shows such an image.

Step 170:

characterization. The sample may be characterized on the basis of theelementary diffraction patterns generated thereby. When the samplecontains diffracting particles 10 b, they may be characterized on thebasis of the diffraction patterns associated with each particle, as theyappear in the high-resolution image I_(HR). Such a characterization maybe carried out directly on the basis of each elementary diffractionpattern, for example by morphological analysis, or by applying anumerical reconstruction algorithm to the high-resolution image I_(HR),as described below.

As described with reference to the prior art, it is possible to apply,to each image I_(i) acquired by the image sensor 16, or to thehigh-resolution image I_(HR) described above, a propagation operator h,so as to calculate a quantity representative of the light wave 22transmitted by the sample 10, and to which the image sensor 16 isexposed. Such a method, which is said to be a holographic-reconstructionmethod, notably allows an image of the modulus or of the phase of thelight wave 22 to which the image sensor is exposed to be reconstructedin a reconstruction plane parallel to the detection plane P₀, andnotably in the plane P₁₀ in which the sample lies. To do this, the imagein question is convoluted with a propagation operator h. It is thenpossible to reconstruct a complex expression A for the light wave 22 atany point in space of coordinates (x, y, z), and in particular in areconstruction plane P_(z) located at a distance |z| from the imagesensor 16, this reconstruction plane possibly being the plane P₁₀ of thesample. The complex expression A is a complex quantity the argument andthe modulus of which are respectively representative of the phase andintensity of the light wave 22 to which the image sensor 16 is exposed.The convolution with the propagation operator h allows a complex imageA_(z) representing a spatial distribution of the complex expression A ina plane, called the reconstruction plane P_(z), lying at a coordinate zfrom the detection plane P₀, to be obtained. In this example, thedetection plane P₀ has as equation z=0. The complex image A_(z)corresponds to a complex image of the sample in the reconstruction planeP_(z). It also represents a two-dimensional spatial distribution of theoptical properties of the wave 22 to which the image sensor 16 isexposed.

The function of the propagation operator h is to describe thepropagation of light between the image sensor 16 and a point ofcoordinates (x, y, z), which point is located at a distance |z| from theimage sensor. It is then possible to determine the modulus M(x, y, z)and/or the phase φ(x, y, z) of the light wave 22, at this distance |z|,which is called the reconstruction distance, with:M(x,y,z)=abs[A(x,y,z)]φ(x,y,z)=arg[A(x,y,z)]The operators abs and arg are the modulus and argument, respectively.

In other words, the complex amplitude A of the light wave 22 at anypoint in space of coordinates (x, y, z) is such that: A(x, y, z)=M(x, y,z)e^(jφ(x, y, z)). On the basis of such reconstructions, it is notablypossible to form what are called reconstructed images, of the modulus(modulus image or amplitude image) or the phase (phase image),respectively from the modulus M(x, y, z) and phase φ(x, y, z)reconstructed at a given distance Z.

Experimental trials have been carried out using a sample containingwater, in which silica particles of 3 μm and 6 μm diameter weresubmerged. The sample is a fluidic chamber of 100 μm thickness.

The main experimental parameters were the following:

-   -   light source: CivilLaser laser diode centered on 405 nm;    -   VFU-J003-MB 8-bit CMOS sensor, 3884×2764 square pixels of 1.67        μm side length;    -   piezoelectric module: Kingstate KMTG1303-1 buzzer, stops being        placed in order to oppose a movement of the sensor along the        axis Z;    -   distance between the light source and the sample: 8 cm;    -   distance between the sample and the image sensor: 1.5 mm.

The algorithm described with reference to steps 100 to 170 was appliedso as to obtain 16 acquired images I_(i) and to form one high-resolutionimage I_(HR). FIG. 4 shows each movement δ_(i) between the acquisitionof two successive images I_(i−1), I_(i).

FIGS. 5A, 5B and 5C respectively show an acquired image I_(i), asubpixelated image I_(i,HR) resulting from the image shown in FIG. 5A,and the high-resolution image I_(HR) obtained at the end of the process.Two diffraction patterns may be clearly seen in the central portion ofthese images.

FIGS. 6A and 6B show the profile of the intensity of the pixels of theimages shown in FIGS. 5A and 5C, each profile being that along thedotted white line shown in said images, respectively. The abscissa axisrepresents the pixel number whereas the ordinate axis represents thevalue of the intensity of each pixel. The standard deviation of eachprofile was calculated. The values obtained are 5.1 and 14 for FIGS. 6Aand 6B, respectively. The profile of FIG. 6B, which is that of thehigh-resolution image, has a higher dispersion with respect to theaverage of the image, this indicating that the diffraction rings of eachdiffraction pattern are better defined.

FIGS. 7A and 7C illustrate images of the modulus M(x, y, z) of theamplitude A(x, y, z) reconstructed in a plane P₁₀ parallel to thedetection plane P₀ and through which the sample 10 passes, these imagesbeing based on the images shown in FIGS. 5A and 5C, respectively. Thesereconstructed images were obtained by implementing the reconstructionalgorithm described above, with z=1.16 mm. The propagation operator is,in this example, the Fresnel-Helmholtz function, such that:

${h\left( {x,y,z} \right)} = {\frac{1}{j\;\lambda\; z}e^{j\; 2\;\pi\frac{z}{\lambda}}{\exp\left( {j\;\pi\frac{x^{2} + y^{2}}{\lambda\; z}} \right)}}$where x, y are coordinates in a plane perpendicular to the propagationaxis Z, i.e. in the detection plane P₀ or in the plane P₁₀ of the sampleand λ is a wavelength, for example the central wavelength, of thespectral band Δλ. Other more refined reconstruction methods may beimplemented, for example those described in patent application FR1652500, filed 23 Mar. 2016.

FIG. 7A shows the result of a reconstruction based on an image I_(i)acquired by the image sensor. It is an example representative of theprior art. FIG. 7C shows the result of a reconstruction based on ahigh-resolution image I_(HR) obtained according to the invention. FIGS.7B and 7D are zooms of regions of interest framed by a black rectanglein FIGS. 7A and 7C, respectively. The object shown is an agglomerationof two spheres of 6 μm diameter and a small sphere of 3 μm diameter. Theimage reconstructed on the basis of the high-resolution image I_(HR) hasa sufficient spatial resolution to allow the three spheres (see FIG. 7D)to be distinguished, this not being the case for the image reconstructedon the basis of the image I_(i) acquired by the image sensor 16 (seeFIG. 7B).

Other trials have been carried out using a sample containing blood.Total blood was subjected to a Dextran-based treatment in order toaggregate red blood cells. After sedimentation of the latter, thesupernatant, containing white blood cells, was collected, then dilutedto 1:10 in a phosphate-buffered saline (PBS) saline buffer. The lightsource was a 4-colour Cree light-emitting diode of reference XLamp MCEColor (white, not used—blue, 450 nm—green, 520 nm—red, 620 nm). Thisdiode comprised 4 elementary diodes, only the elementary diode emittingin the blue being used in this trial. FIGS. 8A, 8C and 8E respectivelyshow:

-   -   an image of the modulus M(x, y, z) of the complex amplitude A(x,        y, z) reconstructed in the plane P₁₀ of the sample, obtained        from an image I_(i) acquired by the image sensor;    -   an image of the modulus M(x, y, z) of the complex amplitude A(x,        y, z) reconstructed in the plane P₁₀ of the sample, obtained        from a high-resolution image I_(HR) obtained by applying steps        100 to 160;    -   the movement Δ_(i) between the acquisition of two successive        I_(i−1), I_(i), images the format employed being similar to that        of FIG. 4.

In FIGS. 8A and 8C, dark spots correspond to white blood cells. FIGS. 8Band 8D are details of a region of interest framed by a box in FIGS. 8Aand 8C, respectively. This allows the improvement in spatial resolutionachieved with the invention to be appreciated. FIG. 8D, which wasobtained by reconstruction on the basis of a high-resolution image, hasan improved spatial resolution with respect to FIG. 8B.

The invention will possibly be employed in the field of biology orhealth, but also in environmental inspection, food processing or otherindustrial processes.

The invention claimed is:
 1. A method for forming an image of a samplecomprising: a) illuminating the sample with a light source; b) acquiringa plurality of images of the sample using an image sensor, the samplebeing placed between the light source and the image sensor, such that:the sample is immobile with respect to the light source between eachacquisition; no magnifying optics are placed between the sample and theimage sensor; the image sensor lies in a detection plane, the imagesensor being moved, in the detection plane, between two successiveacquisitions while the sample is immobile; and each acquired image isrespectively associated with a position of the image sensor in thedetection plane, each position being different from the next, eachacquired image having a field of observation, each acquired imagecontaining pixels; c) calculating a movement of each acquired image withrespect to a reference image in which the image sensor occupies areference position; and d) forming a high-resolution image, from theacquired images and the movement calculated for each thereof, thehigh-resolution image having a field of observation corresponding to anintersection of the fields of observation of each acquired image, thehigh-resolution image containing more pixels than each acquired image,wherein the image sensor is blocked from moving in a directionperpendicular to the detection plane.
 2. The method of claim 1, whereinthe image sensor is securely fastened to a piezoelectric transducer, themovement of the image sensor being generated by activation of thepiezoelectric transducer.
 3. The method of claim 1, wherein the movementof the image sensor between two successive positions is random.
 4. Themethod of claim 1, wherein d) comprises: i) obtaining a stack ofsubpixelated images, each subpixelated image being obtained from anacquired image, the subpixelated image containing a number of pixelshigher than the number of pixels of the acquired image; ii) using themovements determined in c), aligning each subpixelated image so as toobtain a stack of subpixelated and aligned images; and iii) combiningthe subpixelated and aligned images in order to obtain thehigh-resolution image.
 5. The method of claim 1, wherein d) comprises:i) using the movements determined in c), aligning each acquired image soas to obtain a stack of aligned images; ii) obtaining an aligned andsubpixelated image from each aligned image obtained in i), the alignedand subpixelated image containing a number of pixels higher than thenumber of pixels of the aligned image, so as to obtain a stack ofaligned and subpixelated images; and iii) combining the aligned andsubpixelated images in order to obtain the high-resolution image.
 6. Themethod of claim 1, wherein d) comprises: i) aligning each acquired imageusing the movement that is associated therewith, so as to obtain analigned image from each acquired image; and ii) combining each alignedimage to form the high-resolution image.
 7. The method of claim 1,wherein the maximum value of the movement between two successiveacquired images is 5 times or 10 times the distance between two adjacentpixels.
 8. The method of claim 1, comprising: e) applying a numericalpropagation operator to the resulting image and determining a complexamplitude of a light wave to which the image sensor is exposed.
 9. Adevice for producing an image of a sample comprising: a light sourceconfigured to illuminate the sample; an image sensor; the device beingconfigured so that the sample is placed between the light source and theimage sensor, no magnifying optics being placed between the sample andthe image sensor; the image sensor being configured to acquire an image,in a detection plane, of a light wave transmitted by the sample whenilluminated by the light source; the device further comprising: apiezoelectric transducer that is connected to the image sensor and ableto induce a movement of the image sensor in the detection plane withoutmoving the sample; and a processor, configured to process a plurality ofimages, acquired by the image sensor, of the sample, each acquired imagebeing respectively associated with a position of the image sensor in thedetection plane, each position being different from the next; and astrap that blocks the image sensor from moving in a directionperpendicular to the detection plane the processor being configured toimplement c) and d) of the method of claim 1.